Question

The C.P of two watches taken together is Rs.840. If selling one at a Profit of 16% and the other at a loss of 12% there is no loss no gains in the whole transaction, then the C.P of the two watches are respectively.

A) Rs.360, Rs.480
B) Rs.480, Rs.360
C) Rs.380, Rs.460
D) Rs.400, Rs.440

Answer 1

Hint: In this question, we first suppose the cost of watch x. So, second watch (840 – x). According to the question form an equation and then we find the value of x. Using the value of x, find the C.P. of two watches.

Complete step by step solution: Let the cost of one watch = x
So, the cost of second watch = 840 – x
According to the question: It is given that there is no loss or no gain so they are equal
So,
16 % of x = 12 % of (840 – x)
$ \Rightarrow \dfrac{{16}}{{100}} \times x = \dfrac{{12}}{{100}} \times \left( {840 - x} \right)$
$ \Rightarrow \dfrac{{16}}{{100}} \times x = \dfrac{{12 \times 840}}{{100}} - \dfrac{{12x}}{{100}}$
$ \Rightarrow \dfrac{{16x}}{{100}} + \dfrac{{12x}}{{100}} = \dfrac{{12 \times 840}}{{100}}$
⇒ 28x = 12 × 840
$ \Rightarrow x = \dfrac{{12 \times 840}}{{28}}$
x = 360
Hence, cost of first watch = 360
Cost of another watch = 840 – 360 = 480

So, from the above option, only option A is correct.

Note: In this type of question, a linear equation in one variable is formed. Use variable x, find the profit or loss percent in the terms of x, then equate them. We solve for x to find the cost.